Velocity profile for different z positions and x positions in a microchannel

I need some help for this problem. I have the coding as below. How do I get the results for different z positions and x positions of velocity profile in a microchannel? The evaluated velocity field equation is referring to Bruus(2004).

{

 h=100e-6;
 w=100e-6;
 l=50e-3;
 v=2.5e-4;
 z=0;
 i=0;
 y=0;
 while(i<1000)
 n = 1;
 ans=0;
 term=0;
 while (n<1000) 
a=sin(n*pi*z/h);
b=cosh(n*pi*y/h);
c=cosh(n*pi*w/(2*h));
d=(1/(n^3));
e=tanh(n*pi*w/(2*h));
f=(192*h)/((n^5)*(pi^5)*w);
g=(48*v)/(pi^3);
term=(g*d*(1-(b/c))*a)/(1-(f*e));
ans=ans+term;
n=n+2;
end
i=i+1;
result((i+1),1)=ans;
result((i+1),2)=z;
z=w/999*i;
end
xlswrite('Figure6.xlsx',result)
width = xlsread('Figure6.xlsx', 'B:B')
avevelocity = xlsread('Figure6.xlsx', 'A:A') 
plot(width,avevelocity); }

I really appreciate it if someone could answer to my problem. Thank you.

[burak uludag]

Hi everyone I need matlab codes for ADV velocity contour graph,Please help me ...

Answer 1

[Torsten]

You will have to modify your code as follows to fit the Bruus formula: {

 h=100e-6;
 w=100e-6;
 l=50e-3;
 v=2.5e-4;
 z=0;
 i=0;
 y=0;
 while(i<1000)
 n = 1;
 ans1=0;
 ans2=0;
 term1=0;
 term2=0;
 while (n<1000) 
a=sin(n*pi*z/h);
b=cosh(n*pi*y/h);
c=cosh(n*pi*w/(2*h));
d=(1/(n^3));
e=tanh(n*pi*w/(2*h));
f=(192*h)/((n^5)*(pi^5)*w);
g=(48*v)/(pi^3);
term1=g*d*(1-b/c)*a;
term2=f*e;
ans1=ans1+term1;
ans2=ans2+term2;
n=n+2;
end
i=i+1;
result((i+1),1)=ans1/(1-ans2);
result((i+1),2)=z;
z=w/999*i;
end
xlswrite('Figure6.xlsx',result)
width = xlsread('Figure6.xlsx', 'B:B')
avevelocity = xlsread('Figure6.xlsx', 'A:A') 
plot(width,avevelocity); }

Best wishes Torsten.

[Anne Lee]

Thank you. I need to plot the velocity graph at different length locations of the microchannel. What variables in the bruus equation should I change?

[Torsten]

The velocity profile is the same at different length locations (l) in the channel. It only changes with width (w) and height (h).

Best wishes Torsten.

[Anne Lee]

Thanks. I get it now. Is there any possibility to get along x-direction using other method?

[Torsten]

Why do you think the velocity profile should change with the length coordinate ? The profile you calculate above is the developed velocity field that forms in a rectangular channel. Do you mean you want to enter the channel with a non-developed profile and study how it changes over the length until it reaches steady-state ?

Best wishes Torsten.

[Anne Lee]

Yes, exactly. I wish to study how the flow changes along the microchannel length until it reaches steady-state but I don't know how to modified the equation.

[Torsten]

I think to answer this question, you will have to solve the complete three-dimensional Navier-Stokes equations in a rectangular duct numerically (e.g. with OPENFOAM or ANSYS).

Best wishes Torsten.

[Anne Lee]

Oh,I see. Thank you for your time. I am truly appreciate it.

[Anne Lee]

Another question, please.To get the profile changes with width and height, I need to change the variables in y and Z. For example, profile at z=35micron & 65micron will have same velocity about 0.46mm/s. I should just change the h value?

[Torsten]

I don't understand your question. Could you clarify ? You should change the h value to get what ?

Best wishes Torsten.

[Anne Lee]

How do velocity profile can be obtained by varying the height or width in the Bruus equation? Which parameters should we consider?

Answer 2

[Torsten]

According to Bruus' notation, keep y fixed and vary z in between 0 and h to get velocity profiles in height direction or keep z fixed and vary y in between -0.5*w and 0.5*w to get velocity profile in length direction. Notice that you will have to set z=h*999/i instead of z=w*999/i in your code above.

Best wishes Torsten.

[Anne Lee]

Thank you. It works!

[Anne Lee]

I can't solve this coding. Result generated is a zero plane. Any idea? Thanks in advance.

{result=0;

y=0;

j=0;

while(j<((w/(10^-6))+1))

i=0;

z=0;

while(i<((h/(10^-6))+1))

n = 1;

ans1= 0;

ans2= 0;

term1= 0;

term2= 0;

while (n<50)

a = sin (n*pi*z/h);

b = cosh (n*pi*abs(y-(w/2))/h);

c = cosh (n*pi*w/(2*h));

d = (1/(n^3));

e = tanh (n*pi*w/(2*h));

f = (192*h)/((n^5)*(pi^5)*w);

g = (48*v)/(pi^3);

term1 = g*d*(1-b/c)*a;

term2 = f*e;

ans1 = ans1+term1;

ans2 = ans2+term2;

n = n+2;

end

result((i+1),(j+1))= (ans1/(1-ans2));

i=i+1;

z=h/(h/10^-6)*i;

end

y=w/(w/(10^-6))*j;

j=j+1;

end

xlswrite('Reg_3D',result);

figure(1);

surfc(result);

shading interp;

colormap(jet);

xlabel('Width(um)');

ylabel('Height(um)');

zlabel('Velocity(m/s)');

formatSpec = '%10.2e\n';

title(['Velocity Profile of',num2str(w,formatSpec),'m x',num2str(h,formatSpec),'m']);

colorbar end}